Batfamily members and DC trinity if exposed to Black Mercy flower
In Superman (1939) Annual #11, Bruce and Clark were both grabbed by a Black Mercy flower. In Batgirl (2009) #24, Steph was taken by one. The Black Mercy tries to keep its victims from escaping by putting them in a perfect world that they don't want to escape or fight and protect people in, so that it can feed off of their still and reasonably relaxed body. I would assume that it uses its victim's memories to create that world, so it's a dream which their brain creates with the Black Mercy pushing in a direction to keep them relaxed, still, and alive until they die from losing too much internal energy to the flower.
Clark's mind created a dream where Krypton and his family there survived. He was married to Lyla Lerrol, who he had met when he visited Krypton in Superman (1939) #141. Even with the dream world's imperfections and unhappiness, that satisfied Clark and kept him from wanting to change the world as he's driven to become Superman because of having lost Krypton and his birth family. Without that loss, he doesn't have the drive to fight and save the world though he still wants to help people. He wants to protect his family in that dream.
Bruce's dream focused on his parents surviving and, as in every in-character version, he doesn't have the drive to become Batman unless he loses his parents or has an external influence. Jason had to free Bruce from the flower as keeping his parents is a perfect world for Bruce. He'd still help people but not as Batman. Detective Comics #500 showed the alternate Bruce becoming Batman because the Batman he met saved his parents and taught him that people can live if a hero is there, similar to the drive May Parker has in her Spider-Girl series but not the drive to prevent tragedies that orphaned Batman has. In Superman & Batman: Generations by John Byrne, Clark's father learns about Batman and informs Bruce's parents of that future and that it only happens if they die. Bruce's parents choose to walk into the alley that Jonathan Kent showed them, believing that Batman is necessary to Gotham and sacrificing themselves to give their son the drive to become that hero. The dream in the 2026 annual for Detective Comics, where Bruce becomes Batman even though his parents survive and he had no one influencing him to become a hero, could lead to Bruce resisting the Black Mercy through his dissatisfaction with the world and need to improve it, but is not what any other Batman story shows. The annual was poorly written and appeared to be focused on glorifying Batman instead of characterizing him.
I'm not certain how the Black Mercy could influence Diana to stay in her dream and not become Wonder Woman and escape. Steve's influence on her is very important to her. Maybe she'd be satisfied eternally staying with her mother on Themyscira but I suspect that leaving to help people everywhere is essential to her satisfaction with life. She'd probably escape the flower on her own.
If Dick got exposed to the Black Mercy, he'd probably dream of his parents surviving and that he'd stay with the circus in his dream. Like Bruce and Clark, any imperfections would lead to him trying to help his family, not the world. I don't think he'd try to escape the flower.
Jason would probably dream of his parents, Catherine and Willis, surviving so that he didn't become homeless. On its own, that would still lead to his being unhappy and fighting to improve Gotham, with or without Batman's influence. If his brain thought of the idea of Willis not getting fired and becoming a criminal, that could lead to the dream Willis remaining a good father and Jason being happy in his dream world.
Tim could easily be satisfied by a dream world where his parents pay more attention to him. School is an enjoyable environment for him and he makes friends easily so he'd have no need to seek out Bruce and become Robin. A perfect world for him would also involve Bruce never losing Jason so he'd have no reason to want to resist the Black Mercy.
Damian has two possibilities. If we run on Grant Morrison's version, with Talia raping Bruce and treating her son horribly, his current mind would never be happy unless he left and fought to change the world, which would force him to fight the Black Mercy. On the other hand, if we run on the current version, where Talia truly cares about Damian and she has the morals from her original appearances, than his dream could involve Talia helping Damian take over the League of Assassins from Ra's and Damian working to improve it. That could satisfy him without him fighting to change the world.
Barbara's Black Mercy-influenced dream would probably be one where she remains a librarian, heroes aren't as necessary to save people, and she remains focused on her job and her father. She'd be willing to let the flower feed on her.
I'm skeptical that Cass could imagine her father not teaching her to become a killer and eventually having her kill someone. In any dream where she's relaxed, she's going to eventually run away from her father with her wish to die, when the flower needs her alive so it can feed off of her. Any world where she survives after her killing Faizul will eventually have her focused on protecting people instead of killing herself and fighting is the only way she knows to do so without external influence. I can't think of a scenario that she could imagine where she doesn't fight to help people as a hero, isn't fundamentally dissatisfied with living, and doesn't escape the Black Mercy's influence.
Steph would need to have a dream where either her mother fights back against her father or her father is a good and caring father to be satisfied with the world but I don't know how she could imagine that situation. Any dream she has would involve her becoming a hero in order to protect her mother, herself, and other people from her father. She'd escape the flower on her own, which agrees with canon.
Duke's parents would never have been attacked by the Joker in his dream. He'd still be involved in organizing and protecting his community but he'd never become Robin or Signal in his dream world.
Helena's dream would probably be one where her family survived. In that dream, she'd be protective of her community but not Gotham as a whole. She'd probably have many arguments with her parents and be trying to make them more of a protective force and less focused on rackets.
My thinking is that Cass, Damian as originally written by Grant Morrison with evil Talia, Princess Diana, and Steph are the only people here who would escape the Black Mercy on their own and become protective heroes even without external influence in any world that they can conceive of. Jason needs a lot of changes early in his life to avoid the need to change the world to be satisfied with it but it's possible that the Black Mercy could dig deeply enough into his memories to create that dream. The others would fall victim to the flower as they needed a push in their lives to gain the drive to make the sacrifices needed to be a hero, though they'd still be very helpful to society and protective of people in other ways.